publication . Article . 2017

Algebraic Ricci Solitons on Metric Lie Groups with Nondiagonalizable Ricci Operator

Клепиков, П.Н.; Родионов, Е.Д.;
Open Access Russian
  • Published: 22 May 2017 Journal: Izvestiya of Altai State University (issn: 1561-9451, eissn: 1561-9443, Copyright policy)
  • Publisher: Izvestiya of Altai State University
Abstract
In recent years, various generalizations of Einstein manifolds are actively studied, for example, manifolds with the trivial Schouten-Weyl tensor, and Ricci solitons, which were first considered by R. Hamilton. Ricci solitons on homogeneous (pseudo)Rieman-nian spaces and, in particular, on the Lie groups have been studied by many mathematicians. For example, there are no nontrivial homogeneous invariant Ricci solitons on three and four-dimensional Lie groups with a left-invariant Riemannian metric. A similar result was proved for the unimodular Lie groups with a left-invariant Riemannian metric in any dimension. However, this question is still an open problem fo...
Subjects
arXiv: Mathematics::Differential GeometryMathematics::Metric Geometry
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